Setting Up a Replica Exchange Approach to Motif Discovery in DNA Jeffrey Goett Advisor: Professor Sengupta

Protein Synthesis from DNA Translation to Proteins Transcription Regulation RNA polymerase Binding Proteins gene Binding sites

Binding Sites Sequence A: code for protein Binding protein “A” Binding Site A - A - C - G - A - C - T - T - G - C - T - G - T - T - C - A - A - C - C - A - A - A - G - T - T - G - G - T - Sequence B: code for protein A - A - G - G - A - C - T - T - C - C - T - G - C - G - T - T - G - C - T - C - G - C - A - A - C - G - A - G - Binding protein “A”

Discovering New Binding Motifs …ATCG GCTCAG CTAG… …CACT GATCAG AGTA… …TTCC GCTCTG TAAC… …GCTA GCTCAA ATCG… Motif Probability Model Motif: GCTCAG

Modeling Motifs in Sequences ATATCCGTA AATCGAGAC TCGATGTGT CCACCTGCA Assume: Break into N sequences Each sequence has one instance of motif embedded in random background Variations of motif by point mutation, but not insertion or deletion

Modeling Motifs in Sequences AT ATC CGTA A ATC GAGAC TCG ATG TGT CC ACC TGCA The “Alignment:” Starting position of motif in each sequence The “Motif Probability Distribution:” Probability of each letter occurring at each motif position

Scoring a Model “Log-likelihood” score: ATATCCGTA AATCGAGAC TCGATGTGT CCACCTGCA p 1,T p 2,A p 3,T p 1,A p 2,G p 3,A p 1,A p 2,T p 3,G p 1,C p 2,C p 3,A p C p C p G p T p A pApA 0 p A p A p T p C p G pCpC 0 p T p C p G p T p G p T p C p C p T p G p C p A 0 0 0

Example Models A TAT CCGTA AAT CGA GAC TCGATG TGT CC ACC TGCA {3, 2, 4, 3} AT ATC CGTA A ATC GAGAC TCG ATG TGT CC ACC TGCA {2, 4, 7, 3}

The Gibbs Sampler We want to find that maximizes

The Gibbs Sampler

Times visited Over time, the frequency distribution approaches

Biasing our search to these areas may discover the pj,ro values which maximize faster. If we assume areas of local maximization contribute the most during “integration” to the local maximizations of Optimization Technique

Multiple Gibbs Samplers By combining results from Gibbs Samplers begun at random positions, find maximizing sooner

Replica Exchange/Parallel Tempering “Low-sensitivity” samplers which “scout out area” periodically swap with “high-sensitivity” samplers good at focused searches if swap appears promising.

Controlling Sensitivity Adjust the relative probability of sampling an x i by adjusting a new parameter in distribution: Small Large Search breadth of space Focused search of region

Testing the Sensitivity Running on randomly generated sequences to see motifs found, different sensitivity samplers converge to different scores. Betas

Predicting Convergence Score Measure of Similarity: magnetization “Configuration Score:” energy Ex: m=.5 m=.5 E=0 m=1 E=-6J m=0 E=2J m=0 E=2J m=0 E=2J

Alignment Analogue m=.77 E=-5J m=1 E=-9J m=.77 E=-5J m=.77 E=-5J A: B: C:

Test Results L < |alphabet| w

Test Results L > |alphabet| w

Test Results

Hidden Motifs: Gibbs Sampler Beta =.1Beta =.5Beta =.9 Beta = 1.3Beta = 1.7Beta = 2 W=5, l=500

Hidden Motifs: Replica Exchange Betas